//
//---------------------  1D  ---------------------
//
//
// Quick is not defined for 1D
//

//
//---------------------  3D  ---------------------
//
//       Staggered Mesh for w-vel and v-vel
//
//   0       1       2       3       4       5   
//
//5      >       >       >       >       > 
//       |       |       |       |       |              
//   ^---+---^---+---^---+---^---+---^---+---^  4       Mesh for scalar fields
//       |       |       |       |       | 
//4      >   o   >   o   >   o   >   o   >               5  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |               4  x o | o | o | o x
//   ^---+---^---+---^---+---^---+---^---+---^  3           +---+---+---+---+
//       |       |       |       |       |               3  x o | o | o | o x
//3      >   o   >   o   >   o   >   o   >                  +---+---+---+---+
//       |       |       |       |       |               2  x o | o | o | o x
//   ^---+---^---+---^---+---^---+---^---+---^  2           +---+---+---+---+
//       |       |       |       |       |               1  x o | o | o | o x
//2      >   o   >   o   >   o   >   o   >               0  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |                  
//   ^---+---^---+---^---+---^---+---^---+---^  1           0 1   2   3   4 5 
//       |       |       |       |       |                 
//1      >   o   >   o   >   o   >   o   >                 o central node
//       |       |       |       |       |                 x boundary node
//   ^---+---^---+---^---+---^---+---^---+---^  0          > w velocity 
//       |       |       |       |       |                 ^ v velocity
//0      >       >       >       >       >    
//       0       1       2       3       4             
//
//                                                  
//          Volumes for w-velocity
//
//   0       1       2       3       4       5
//
//5      >       >       >       >       > 
//       :       :       :       :       :              
//   ^...+---^---+---^---+---^---+---^---+...^  4       Mesh for scalar fields
//       |   |   :   |   :   |   :   |   | 
//4      >   o   >   o   >   o   >   o   >               5  x-x-+-x-+-x-+-x-x
//       |   |   :   |   :   |   :   |   |               4  x o | o | o | o x
//   ^...+---^---+---^---+---^---+---^---+...^  3           +---+---+---+---+
//       |   |   :   |   :   |   :   |   |               3  x o | o | o | o x
//3      >   o   >   o   >   o   >   o   >                  +---+---+---+---+
//       |   |   :   |   :   |   :   |   |               2  x o | o | o | o x
//   ^...+---^---+---^---+---^---+---^---+...^  2           +---+---+---+---+
//       |   |   :   |   :   |   :   |   |               1  x o | o | o | o x
//2      >   o   >   o   >   o   >   o   >               0  x-x-+-x-+-x-+-x-x
//       |   |   :   |   :   |   :   |   |                  
//   ^...+---^---+---^---+---^---+---^---+...^  1           0 1   2   3   4 5 
//       |   |   :   |   :   |   :   |   |                 
//1      >   o   >   o   >   o   >   o   >                 o central node
//       |   |   :   |   :   |   :   |   |                 x boundary node
//   ^...+---^---+---^---+---^---+---^---+...^  0          > w velocity 
//       :       :       :       :       :                 ^ v velocity
//0      >       >       >       >       >    
//
//       0       1       2       3       4              
//
//                       
//                  |           |           |           |
//                --^-----------^-----------^-----------^-- 
//                  |     :     |     :     |     :     |               
//                  |     :     | (i,j+1,k) |     :     |
//                  o     >     o    w_N    o     >     o   
//                  |     :     |     :     |     :     |
//                  |     :     |     :     |     :     |
//                --^---------- 3 -- v_n -- 4 ----------^--  4 = v(i+1, j  ,k)
//                  |     :     |     :     |     :     |    3 = v(i  , j  ,k)
//                  |     :     |     :     |     :     |    2 = v(i+1, j-1,k)
//                  o    w_B   w_b   w_P   w_f   w_F    o    1 = v(i  , j-1,k)
//                  | (i,j,k-1) |  (i,j,k)  | (i,j,k+1) |
//                  |     :     |     :     |     :     |
//                --^---------- 1 -- v_s -- 2 ----------^-- 
//                  |     :     |     :     |     :     |               
//                  |     :     |     :     |     :     |
//                  o     >     o    w_S    o     >     o   
//                  |     :     | (i,j-1,k) |     :     |
//                  |     :     |     :     |     :     |
//                --^-----------^-----------^-----------^--
//                  |           |           |           | 
//                   
//   w_b = ( w(i,j,k-1) + w(i,j,k) ) / 2     
//   w_f = ( w(i,j,k+1) + w(i,j,k) ) / 2
//   v_n = ( v(i,j,k) + v(i+1,j,k) ) / 2   
//              3           4
//   v_s = ( v(i,j-1,k) + v(i+1,j-1,k) ) / 2
//              1           2

//   w_e = ( u(i,j,k) + u(i,j+1,k) ) / 2
//   u_w = ( u(i-1,j,k) + u(i-1,j+1,k) ) / 2
// 

namespace Tuna {

template<class Tprec, int Dim>
inline bool Quick_ZCoDi<Tprec, Dim>::calcCoefficients3D () {
    prec_t dyz = dy * dz, dyz_dx = Gamma * dyz / dx;
    prec_t dxz = dx * dz, dxz_dy = Gamma * dxz / dy;
    prec_t dxy = dx * dy, dxy_dz = Gamma * dxy / dz;
    prec_t dxyz_dt = dx * dy * dz / dt;
    prec_t ce, cem, cep, cw, cwm, cwp;
    prec_t cn, cnm, cnp, cs, csm, csp;
    prec_t cf, cfm, cfp, cb, cbm, cbp;

    for (int k = bk; k <= ek; ++k)
	for (int i =  bi; i <= ei; ++i)
	    for (int j = bj; j <= ej; ++j)
	    {
		ce = ( u(i,j,k) + u(i,j+1,k) ) * 0.5 * dyz;
		cw = ( u(i-1,j,k) + u(i-1,j+1,k) ) * 0.5 * dyz;
		cn = ( v(i,j,k) + v(i+1,j,k) ) * 0.5 * dxz;
		cs = ( v(i,j-1,k) + v(i+1,j-1,k) ) * 0.5 * dxz;
		cf = ( w(i,j,k) + w(i,j,k+1) ) * 0.5 * dxy;
		cb = ( w(i,j,k) + w(i,j,k-1) ) * 0.5 * dxy;

		if ( ce > 0 ) { cem = 0.0; cep = ce * 0.125; }
		else {          cem = -ce * 0.125; cep = 0.0; }
		
		if ( cw > 0 ) { cwm = 0.0; cwp = cw * 0.125; }
		else {          cwm = -cw * 0.125; cwp = 0.0; }

		if ( cn > 0 ) { cnm = 0.0; cnp = cn * 0.125; }
		else {          cnm = -cn * 0.125; cnp = 0.0; }
		
		if ( cs > 0 ) { csm = 0.0; csp = cs * 0.125; }
		else {          csm = -cs * 0.125; csp = 0.0; }

		if ( cf > 0 ) { cfm = 0.0; cfp = cf * 0.125; }
		else {          cfm = -cf * 0.125; cfp = 0.0; }
		
		if ( cb > 0 ) { cbm = 0.0; cbp = cb * 0.125; }
		else {          cbm = -cb * 0.125; cbp = 0.0; }

		aE (i,j,k) = dyz_dx - ce * 0.5 + cep - 2 * cem - cwm;
		aW (i,j,k) = dyz_dx + cw * 0.5 + 2 * cwp - cwm + cep; 
		aN (i,j,k) = dxz_dy - cn * 0.5 + cnp - 2 * cnm - csm;
		aS (i,j,k) = dxz_dy + cs * 0.5 + 2 * csp - csm + cnp; 
		aF (i,j,k) = dxy_dz - cf * 0.5 + cfp - 2 * cfm - cbm;
		aB (i,j,k) = dxy_dz + cb * 0.5 + 2 * cbp - cbm + cfp;
		aP (i,j,k) = aE (i,j,k) + aW (i,j,k) + aN (i,j,k) + aS (i,j,k) 
		    + aF (i,j,k) + aB (i,j,k) 
		    + cem - cwp + cnm - csp + cfm - cbp + dxyz_dt;
//			+ (ce - cw);
// Term (ce - cw) is part of discretizated continuity equation, and
// must be equal to zero when that equation is valid, so I can avoid
// this term for efficiency.

		sp(i,j,k) = w(i,j,k) * dxyz_dt - 
		  ( p(i,j,k+1)- p(i,j,k) ) * dxy;
	    
		if (i <= ei-1)        { sp (i,j,k) += cem * w(i+2,j,k); }
		else if ( i == ei) { sp (i,j,k) += cem * w(i+1,j,k); }
		
		if (i >= bi+1)        { sp (i,j,k) -= cwp * w(i-2,j,k); }
		else if ( i == bi) { sp (i,j,k) -= cwp * w(i-1,j,k); }

		if (j <= ej-1)        { sp (i,j,k) += cnm * w(i,j+2,k); }
		else if ( j == ej) { sp (i,j,k) += cnm * w(i,j+1,k); }
		
		if (j >= bj+1)        { sp (i,j,k) -= csp * w(i,j-2,k); }
		else if ( j == bj) { sp (i,j,k) -= csp * w(i,j-1,k); }

		if (k <= ek-1)        { sp (i,j,k) += cfm * w(i,j,k+2); }
		else if ( k == ek) { sp (i,j,k) += cfm * w(i,j,k+1); }
		
		if (k >= bk+1)        { sp (i,j,k) -= cbp * w(i,j,k-2); }
		else if ( k == bk) { sp (i,j,k) -= cbp * w(i,j,k-1); }
	    }    
    calc_dw_3D();
    applyBoundaryConditions3D();
    return 0;     
}


} // Tuna namespace














